Negative Binomial Matrix Factorization for Recommender Systems

Poisson matrix factorization (PF) is a nonnegative matrix factorization (NMF) model (Lee and Seung, 1999) often used for recommender systems (Ma et al., 2011; Gopalan et al., 2015), text information retrieval (Canny, 2004; Buntine and Jakulin, 2006) or dictionary learning for image processing (Cemgil, 2009). The data is assumed to be drawn from the Poisson distribution making it specially well suited for count/integer-valued data. Since the Netflix Prize (Bennett et al., 2007), collaborative filtering (CF) has been giving the state-of-the-art results for recommender systems. CF exploits data relating users to items, like historical data. These data can either be explicit (ratings given by users to items) or implicit (count data from users listening to songs, clicking on web pages, watching videos, etc).